A text-book of Euclid's Elements : for the use of schools : Books I-VI and XI online

may form a regular hexagon.

27. Shew that every section of sphere by a plane is a circle.

28. Find in terms of the length of an edge the radius of a sphere
inscribed in a regular tetrahedron.

29. Find the locus of points in a given plane at which a straight
line of fixed length and position subtends a right angle.

30. A fixed point O is joined to any point P in a given plane
which does not contain O; on OP a point Q. is taken such that the
rectangle OP, OQ is constant: shew that Q lies on a fixed sphere.



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